A new Highly technical Reference Page: The Superiorization Methodology and Perturbation Resilience of Algorithms

The Superiorization Methodology and Perturbation Resilience of Algorithms: A Bibliography

compiled and continuously updated by Yair Censor

This is a (chronologically ordered) bibliography on the superiorization methodology, on perturbation resilience of algorithms and related works, compiled and continuously updated by Yair Censor. If you know of a related work in any form (preprint, reprint, journal publication, conference report, abstract or poster, book chapter, thesis, etc.) that should be included here kindly write to me on: yair@math.haifa.ac.il with full bibliographic details, a DOI if available, and a PDF copy of the work if possible. Copyright notice: Downloads are supplied for personal academic use only. A download is considered equivalent to a pre-print or re-print request. Use is granted consistent with fair-use of a pre-print or re-print. By downloading any of the following materials you are agreeing to these terms.

The superiorization methodology works by taking an iterative algorithm, investigating its perturbation resilience, and then using proactively such perturbations in order to "force" the perturbed algorithm to do in addition to its original task something useful. The perturbed algorithm is called the "superiorized version" of the original unperturbed algorithm. If the original algorithm is computationally efficient and useful in terms of the application at hand, and if the perturbations are simple and not expensive to calculate, then the advantage of this method is that, for essentially the computational cost of the original algorithm, we are able to get something more by steering its iterates according to the perturbations.

This is a very general principle, which has been successfully used in some important practical applications such as image reconstruction from projections, intensity-modulated radiation therapy and nondestructive testing, and awaits to be implemented and tested in additional fields. An important case is when the original algorithm is a feasibility-seeking algorithm, or one that strives to find constraint-compatible points for a family of constraints, and the perturbations that are interlaced into the original algorithm aim at reducing (not necessarily minimizing) a given merit function.

To a novice on the superiorization methodology and perturbation resilience of algorithms we recommend to read first the recent reviews in [22] and [33] below. For a recent detailed description of superiorization-related previous work we direct the reader to Section 3 of [21] below.